A Comparison of Methods for Representing and Aggregating Uncertainties Involving Sparsely Sampled Random Variables - More Results 2013-01-0946

This paper discusses the treatment of uncertainties corresponding to relatively few samples of random-variable quantities. The importance of this topic extends beyond experimental data uncertainty to situations involving uncertainty in model calibration, validation, and prediction. With very sparse samples it is not practical to have a goal of accurately estimating the underlying variability distribution (probability density function, PDF). Rather, a pragmatic goal is that the uncertainty representation should be conservative so as to bound a desired percentage of the actual PDF, say 95% included probability, with reasonable reliability. A second, opposing objective is that the representation not be overly conservative; that it minimally over-estimate the random-variable range corresponding to the desired percentage of the actual PDF. The presence of the two opposing objectives makes the sparse-data uncertainty representation problem an interesting and difficult one. The performance of a variety of uncertainty representation techniques is tested and characterized in this paper according to these two opposing objectives. Some test problems and results are presented from a study currently underway.